For the third day running, the fallout from Michael Gove's decision to remove Labour peer and former Blair adviser Sally Morgan as the chair of Ofsted is leading the headlines. The Lib Dems are warning that they will veto any attempt by him to appoint Tory donor Theodore Agnew as her successor, Labour has written to Jeremy Heywood demanding an investigation, and former Ofsted chief inspector David Bell has warned Gove not to "believe his own hype" in a written rebuke.

Few voters will trouble themselves with the details (how many know or care who leads Ofsted?) but the repeated criticisms of Gove from all sides will encourage the suspicion that the education system is being changed in undesirable ways - and that should trouble the Tories. While the Education Secretary is lauded by the commentariat and by Conservative activists, his approval rating among parents is less impressive. A YouGov poll last year found that 25 per cent of voters would be less likely to vote Tory if he became leader with just four per cent more likely.

And voters, contrary to Westminster perception, aren't keen on his policies either. Another YouGov poll, for the Times, showed that just 27 per cent support free schools with 47 per cent opposed. In addition, 66 cent share Labour and the Lib Dems' belief that the schools should only be able to employ qualified teachers and 56 per cent believe the national curriculum should be compulsory. For these reasons, among others, Labour has consistently led the Tories (see p. 8) on education since the end of 2010, with a five point advantage at present.

Worse, just 12 per cent of teachers (at far from insignificant voting group) would vote Conservative, compared to 43 per cent for Labour and 6 per cent for the Lib Dems. Evidence of why was supplied elsewhere in the poll, which found that 79 per cent believe that the government's impact on the education system has been negative, and that 82 per cent of teachers and 87 per cent of school leaders are opposed to the coalition's expansion of academies and free schools. In addition, 74 per cent said that their morale had declined since the election and 70 per cent of head teachers did not feel trusted by ministers to get on with their jobs. Finally, 91 per cent of teachers opposed publicly-funded schools being run for profit (a policy Gove has said he would consider introducing under a Conservative majority government) and 93 per cent believed academies and free schools should only employ teachers with Qualified Teacher Status.

Those who believe that the Tories derive a political dividend from Gove's clashes with "the blob" (the name he and his ideological allies use for the educational establishment after the 1958 horror film) forget that voters are far more likely to trust teachers than they are politicians. A poll by Ipsos MORI last year found that 86 per cent of voters trust teachers compared to just 18 per cent for politicians (but 41 per cent for trade union officials).

As David Bell writes in his piece today, "Don’t believe your own hype. Whitehall has a habit of isolating ministers. The day-to-day grind of policy battles, firefighting and political ding-dong can start to cut you off from outside ideas and thinking. The row over Ofsted's shows the importance of retaining, and being seen to retain, independent voices near the top – not simply 'yes men'. The danger is that while The Blob is a useful political tool in the short-term, it simply might not be as deep-rooted as the education secretary believes."

Gove has an important message to deliver today on breaking down "the Berlin Wall" between state and private schools (the subject of this week's NS cover story by David and George Kynaston). But his permanent kulturkampf with teachers means that, on this issue and much else, he is danger of no drowning his own words out.